1. The holiday season is always the busiest for e-commerce businesses, with the most sales and biggest discounts. One research claims that there were more online shoppers n 2017 compared to 2016.  In 2017, 800 customers were asked “Did you shop online during the holiday season?” 584 replied “yes” and 216 replied “no”. In 2016, 600 customers were asked “Did you shop online during the holiday season?”  423 replied “yes” and 177 replied “no”. Test the claim at the significant level α=0.01.
   1. State the null hypothesis and the alternative hypothesis. Make sure you clearly indicate the parameters for “year 2017” or “year 2016”:              

   2. H0:

                    Ha:

   3. Find the sample proportion for 2017, the sample proportion for 2016, and the grand proportion.
   4. Calculate the test statistic. Specify which test statistic you are finding (“z” or “t”).
   6. Find the p-value using the appropriate table. Be sure to include any appropriate degrees of freedom.   Draw the curve showing p-value, critical value(s), and rejection region.
   8. What is your decision and interpret the decision. Make sure to include the weight of the evidence, the conclusion, and the significance level.
   10. What is the 80% confidence interval of the difference in percentages of online shopping for 2017 and 2016? Interpret your result(s).

Buckeye Creek Amusement Park is open from the beginning of May to the end of October. Buckeye Creek relies heavily on the sale of season passes. The sale of season passes brings in significant revenue prior to the park opening each season, and season pass holders con- tribute a substantial portion of the food, beverage, and novelty sales in the park. Greg Ross, director of marketing at Buckeye Creek, has been asked to develop a targeted marketing campaign to increase season pass sales. Greg has data for last season that show the number of season pass holders for each zip code within 50 miles of Buckeye Creek. he has also obtained the total population of each zip code from the U.S. Census bureau website. Greg thinks it may be possible to use regression analysis to predict the number of season pass holders in a zip code given the total population of a zip code. If this is possible, he could then conduct a direct mail campaign that would target zip codes that have fewer than the expected number of season pass holders. *I only need help with #5,6,7 thank you

Managerial Report

1. Compute descriptive statistics and construct a scatter diagram for the data. Discuss your findings.

2. Using simple linear regression, develop an estimated regression equation that could be used to predict the number of season pass holders in a zip code given the total population of the zip code.

3. Test for a significant relationship at the .05 level of significance.

4. Did the estimated regression equation provide a good fit?

5. Use residual analysis to determine whether the assumed regression model is appropriate.

6. Discuss if/how the estimated regression equation should be used to guide the marketing campaign.

7. What other data might be useful to predict the number of season pass holders in a zip code?

The annual salary of fresh college graduates is thought to be normally distributed with a mean of $45,000 and standard deviation of $8000. Do the following.

(a) What is the z −score of the salary of $55,000? (10 points) (b)

If you randomly select such a graduate, what is the probability that he/she will be earning a salary of $55,000 or less? (Use z −score and Excel function to calculate this) (10 points)

(c) If you randomly select such a graduate, what is the probability that he/she will be earning a salary between $40,000 and $58,000? (Excel function for regular normal distribution to calculate this) (15 points)

Describe the assumptions that should be met when deciding to use the t-test (i.e., scale of measurement; assumptions about variances of groups being compared; assumptions about group sizes; shapes of distributions.)

8. (15 pts) The minimal Brinell hardness for a specific grade of ductile iron is 130. An engineer has a sample of 25 pieces of this type of iron that was subcritically annealed with the Brinell hardness values as given below. The engineer would like to know whether this annealing process results in the proper Brinell hardness on average.

   135 149 132 142 124 130 122 128 120 128 127 123 136 141 130 139 134 135 130 141 149 137 137 140 148

   State the appropriate hypotheses; conduct a hypothesis test using α = 0.05 utilizing the classical approach, confidence interval approach, or p-value approach; state the decision regarding the hypotheses; and make a conclusion.

8. (15 pts) A person’s Intelligence Quotient (IQ) is determined via a series of test questions. The IQ score itself is designed to be approximately normally distributed with a mean value of 100 and a standard deviation of 15. In a sample of 20 students with behavioral problems, a school administrator observes an average IQ of 102.7. The administrator believes that students with behavioral issues have a different cognition from their peers, and thus a different average IQ. State the appropriate hypotheses; conduct a hypothesis test using α = 0.05 utilizing the classical approach, confidence interval approach, or p-value approach; state the decision regarding the hypotheses; and make a conclusion.

A recent study of two vendors of desktop personal computers reported that out of 858 units sold by Brand A, 126 required repair, while out of 779 units sold by Brand B, 97 required repair. Round all numeric answers to 4 decimal places.

1. Calculate the difference in the sample proportion for the two brands of computers, ?̂ ??????−?̂ ?????? = .

2. What are the correct hypotheses for conducting a hypothesis test to determine whether the proportion of computers needing repairs is different for the two brands.

A. ?0:??−??=0, ??:??−??<0 B. ?0:??−??=0, ??:??−??>0 C. ?0:??−??=0, ??:??−??≠0

3. Calculate the pooled estimate of the sample proportion, ?̂ =

4. Is the success-failure condition met for this scenario? A. Yes B. No

5. Calculate the test statistic for this hypothesis test. =

6. Calculate the p-value for this hypothesis test, p-value = .

7. Based on the p-value, we have:

A. very strong evidence

B. extremely strong evidence

C. strong evidence

D. little evidence

E. some evidence that the null model is not a good fit for our observed data.

8. Compute a 90 % confidence interval for the difference ?̂ ??????−?̂ ?????? = ( , )

1.The following probability distribution lists the probability of getting a certain number of questions correct on a five question True/False quiz.

Five-question true/false quiz

( x = number correct)

x P(x)

0 0.03125

1 0.15625

2 0.3125

3 0.3125

4 0.15625

5 0.03125

1A. What is the mean of the probability distribution?

1B. What is the standard deviation?

1C. What is the probability of getting more than 3 questions correct?

2.

2A. The probability that a student passes a certain math exam in 0.7. If the exam is given to 15 students, find the probability that at least 12 of them pass? Hint: This is binomial calculator

2B.On a typical day a credit union opens 5 new accounts. Find the probability that the credit union opens exactly 6 accounts in the next two days. Hint: Use Poisson calculator

Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 123000 dollars. Assume the standard deviation is 37000 dollars. Suppose you take a simple random sample of 69 graduates. Find the probability that a single randomly selected salary is less than 126000 dollars. Answer = Find the probability that a sample of size n = 69 is randomly selected with a mean that is less than 126000 dollars. Answer = Enter your answers as numbers accurate to 4 decimal places.

1. Over a period of 100 randomly chosen trading days in 1993, a basket of small growth stocks returned an average of 13.37% while a basket of diversified stocks returned an average of 19.63%. The standard deviations were 20.39% and 12.85% respectively. On average, did these two investment vehicles produce significantly different returns? Test at the 0.05 level of significance

More than 100 million people around the world are not getting enough sleep; the average adult needs between 7.5 and 8 hours of sleep per night. College students are particularly at risk of not getting enough shut-eye.

A recent survey of several thousand college students indicated that the total hours of sleep time per night, denoted by the random variable X, can be approximated by a normal model with E(X) = 6.94 hours and SD(X) = 1.27 hours.

Question 1. Find the probability that the hours of sleep per night for a random sample of 4 college students has a mean x between 6.71 and 6.95.

(use 4 decimal places in your answer)

Question 2. Find the probability that the hours of sleep per night for a random sample of 16 college students has a mean x between 6.71 and 6.95.

(use 4 decimal places in your answer)

Question 3. Find the probability that the hours of sleep per night for a random sample of 25 college students has a mean x between 6.71 and 6.95.

(use 4 decimal places in your answer)

Question 4. The Central Limit Theorem was needed to answer questions 1, 2, and 3 above.

True or False?

The heights of European 13-year-old boys can be approximated by a normal model with mean μ of 63.6 inches and standard deviation σ of 2.5 inches.

Question 1. What is the probability that a randomly selected 13-year-old boy from Europe is taller than 65 inches?

(use 4 decimal places in your answer)

Question 2. A random sample of 4 European 13-year-old boys is selected. What is the probability that the sample mean height x is greater than 65 inches?

(use 4 decimal places in your answer)

Question 3. A random sample of 9 European 13-year-old boys is selected. What is the probability that the sample mean height x is greater than 65 inches?

(use 4 decimal places in your answer)

Question 4. The Central Limit Theorem was needed to answer questions 1, 2, and 3 above.

True or False?

An exhaustive study of all active Facebook accounts was recently conducted by Facebook. One variable Facebook recorded was the number of friends X of each Facebook user. Suppose X has expected value E(X) = 187 and standard deviation SD(X) = 283.6. Since the possible values of X are only integers and since the distribution of X is highly skewed to the right, the distribution of X cannot be described by a normal model. Suppose you select a random sample of 35 Facebook users and record the number of Facebook friends each user has.

Question 1. What is the probability that the 35 Facebook users in your sample have a sample mean number of friends x greater than 168?

(use 4 decimal places in your answer)

Question 2. What is the probability that the 35 Facebook users in your sample have a sample mean number of friends x less than 197?

(use 4 decimal places in your answer)

Question 3. The Central Limit theorem was needed to answer questions 1 and 2 above.

True or False?   

Please use ONLY one Excel file to answer the below questions. ( including the formula using for Excel)

In 2011, when the Gallup organization polled investors, 34% rated gold the best long-term investment. In April of 2013 Gallup surveyed a random sample of U.S. adults. Respondents were asked to select the best long-term investment from a list of possibilities. Only 241 of the 1005 respondents chose gold as the best long-term investment. By contrast, only 91 chose bonds.

1. Compute the standard error for each sample proportion. Compute and describe a 95% confidence interval in the context of the question.
2. Do you think opinions about the value of gold as a long-term investment have really changed from the old 34% favorability rate, or do you think this is just sample variability? Explain.
3. Suppose we want to increase the margin of error to 3%, what is the necessary sample size?
4. Based on the sample size obtained in part c, suppose 120 respondents chose gold as the best long-term investment. Compute the standard error for choosing gold as the best long-term investment. Compute and describe a 95% confidence interval in the context of the question.
5. Based on the results of part d, do you think opinions about the value of gold as a long-term investment have really changed from the old 34% favorability rate, or do you think this is just sample variability? Explain.

Thank you in advance!

In epidemiology, why is it important to orient the data by person, place and time? What does it mean and what do we learn from this?